Answer:
x² + 5x + 6
Step-by-step explanation:
Foil means first, outside, inside, last
First: (x+2)(x+3)
x × x = x²
Inside: (x+2)(x+3)
x × 3 = 3x
Ouside: (x+2)(x+3)
2 × x = 2x
Last: (x+2)(x+3)
2 × 3 = 6
adding them together:
x² + 3x + 2x + 6 = x² + 5x + 6
95141 1404 393
Answer:
- arc BC: 8.55 cm
- chord BC: 8.03 cm
Step-by-step explanation:
The length of an arc that subtends central angle α will be ...
s = rα . . . . where α is in radians
The central angle BOC is twice the measure of angle QBC, so is 70°, or 7π/18 radians. So, the length of arc BC is ...
s = (7 cm)(7π/18) ≈ 8.55 cm . . . arc BC
__
For central angle α and radius r, the chord subtending the arc is ...
c = 2r·sin(α/2)
c = 2(7 cm)sin(35°) ≈ 8.03 cm . . . . chord AB
![\begin{gathered} a=41.50 \\ b=35.78 \\ B=40.76\text{ \degree} \\ \end{gathered}](https://tex.z-dn.net/?f=%5Cbegin%7Bgathered%7D%20a%3D41.50%20%5C%5C%20b%3D35.78%20%5C%5C%20B%3D40.76%5Ctext%7B%20%5Cdegree%7D%20%5C%5C%20%20%5Cend%7Bgathered%7D)
Explanation
Step 1
a) let
![\begin{gathered} A=49.23\text{ \degree} \\ c=54.8\text{ \degree} \end{gathered}](https://tex.z-dn.net/?f=%5Cbegin%7Bgathered%7D%20A%3D49.23%5Ctext%7B%20%5Cdegree%7D%20%5C%5C%20c%3D54.8%5Ctext%7B%20%5Cdegree%7D%20%5Cend%7Bgathered%7D)
b) b value
to find the measure of side b we can use cosine function
![\begin{gathered} cos\theta=\frac{adjacent\text{ side}}{hypotenuse} \\ replace \\ cos\text{ 49.23=}\frac{b}{54.8} \\ b=54.8*cos49.23 \\ b=35.78 \end{gathered}](https://tex.z-dn.net/?f=%5Cbegin%7Bgathered%7D%20cos%5Ctheta%3D%5Cfrac%7Badjacent%5Ctext%7B%20side%7D%7D%7Bhypotenuse%7D%20%5C%5C%20replace%20%5C%5C%20cos%5Ctext%7B%2049.23%3D%7D%5Cfrac%7Bb%7D%7B54.8%7D%20%5C%5C%20b%3D54.8%2Acos49.23%20%5C%5C%20b%3D35.78%20%5Cend%7Bgathered%7D)
c) angle B
to find the measure of Angle B we can use sine function
![\begin{gathered} sin\theta=\frac{opposite\text{ side}}{hypotenuse} \\ replace \\ sin\text{ B=}\frac{35.78}{54.8} \\ sin\text{ B= 0.65}\Rightarrow inverse\text{ function to isolate B} \\ B=\sin^{-1}(0.65) \\ B=40.76 \end{gathered}](https://tex.z-dn.net/?f=%5Cbegin%7Bgathered%7D%20sin%5Ctheta%3D%5Cfrac%7Bopposite%5Ctext%7B%20%20side%7D%7D%7Bhypotenuse%7D%20%5C%5C%20replace%20%5C%5C%20sin%5Ctext%7B%20B%3D%7D%5Cfrac%7B35.78%7D%7B54.8%7D%20%5C%5C%20sin%5Ctext%7B%20B%3D%200.65%7D%5CRightarrow%20inverse%5Ctext%7B%20function%20to%20isolate%20B%7D%20%5C%5C%20B%3D%5Csin%5E%7B-1%7D%280.65%29%20%5C%5C%20B%3D40.76%20%5Cend%7Bgathered%7D)
d) side a
![\begin{gathered} sin\theta=\frac{opposite\text{ side}}{hypotenuse} \\ sin\text{ A=}\frac{a}{c}=\frac{\placeholder{⬚}}{\placeholder{⬚}} \\ sin\text{ 49.23=}\frac{a}{54.8} \\ multiply\text{ both sides by 54.8} \\ 54.8s\imaginaryI n\text{49.23=}\frac{a}{54.8}*54.8 \\ 41.50=a \end{gathered}](https://tex.z-dn.net/?f=%5Cbegin%7Bgathered%7D%20sin%5Ctheta%3D%5Cfrac%7Bopposite%5Ctext%7B%20side%7D%7D%7Bhypotenuse%7D%20%5C%5C%20sin%5Ctext%7B%20A%3D%7D%5Cfrac%7Ba%7D%7Bc%7D%3D%5Cfrac%7B%5Cplaceholder%7B%E2%AC%9A%7D%7D%7B%5Cplaceholder%7B%E2%AC%9A%7D%7D%20%5C%5C%20sin%5Ctext%7B%2049.23%3D%7D%5Cfrac%7Ba%7D%7B54.8%7D%20%5C%5C%20multiply%5Ctext%7B%20both%20sides%20by%2054.8%7D%20%5C%5C%2054.8s%5CimaginaryI%20n%5Ctext%7B49.23%3D%7D%5Cfrac%7Ba%7D%7B54.8%7D%2A54.8%20%5C%5C%2041.50%3Da%20%5Cend%7Bgathered%7D)
so, the answer is
![\begin{gathered} a=41.50 \\ b=35.78 \\ B=40.76\text{ \degree} \\ \end{gathered}](https://tex.z-dn.net/?f=%5Cbegin%7Bgathered%7D%20a%3D41.50%20%5C%5C%20b%3D35.78%20%5C%5C%20B%3D40.76%5Ctext%7B%20%5Cdegree%7D%20%5C%5C%20%20%5Cend%7Bgathered%7D)
I hope this helps you
Answer:
D.) 1/4
Step-by-step explanation:
6/9 x 3/8
6(3) /8(9)
= 18/72
18/18=1
72/18=4
= D.) 1/4